There appear to be three different words in Tanach that are translated as "a corner":

Pinah (shmot 26:2)

Kanaf (Shmu'el 1 24:4)

Keren (I haven't found one yet, but this site says that its use as "corner" is biblical).

Each word has other uses (leaders, wings, horns among others). Is there discussion why, in any particular pasuk, one of these would be used for "corner" as opposed to any other? Do the secondary meanings consistently import any specific subtleties to the meaning?

Keren might be from קרנות המזבח which are in the corners but also look like horns.
– HeshyJan 15 at 14:29

I’m not sure I agree with the site you, er, cite. I think it’s referring to the usage in the sense of Vayikra 4:7, where קרן refers to the corners of the Mizbeiach, but the word really refers to a protrusion (hence its common meaning of “horn”) and here refers to the fact that there were vertical pillars at the corners of the Mizbeiach.
– DonielFJan 15 at 14:32

@DonielF that was my sense also -- I went through other uses and couldn't find anything explicitly and discretely "corner" but that web page made the assertion so I rolled with it.
– rosendsJan 15 at 14:41

The entry for פנה, pages 202-203, interprets the root as “turn to and focus attention.” Usage #8 is the one relevant here: “corner; walls joined from different directions” (emphasis mine). In other words: the word פינה, when used in the sense of a corner, refers to an interior corner.

The entry for כנף, page 120, interprets the root as “cover and conceal from view.” Usage #4 is the one relevant here: “corner; edge” (emphasis still mine). Seemingly, the distinction between כנף and פינה is the difference between the corner of a room versus the corner of a garment or a wing (I actually don’t see this usage in any other sense).

The entry for קרן, page 233, interprets the root as “project upwards.” Usage #4 is the one relevant here: “corner elevations” (emphasis still-okay, you get the point). Here the distinction seems to be not just any type of corner, but one that goes upwards, unlike the interior corner of a room or the flat corner on an edge.